Related papers: Weak solutions to problems involving inviscid flui…
We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an…
In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow…
Using a recent result of C. De Lellis and L. Sz\'{e}kelyhidi Jr. we show that, in the case of periodic boundary conditions and for dimension greater or equal 2, there exist infinitely many global weak solutions to the incompressible Euler…
We consider a model for an incompressible visoelastic fluid. It consists of the Navier-Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature…
We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least $2$) to exact weak solutions. The method is closely related to the incompressible…
We consider the governing equations for the motion of the inviscid fluids in two moving domains and an evolving surface from an energetic point of view. We employ our energetic variational approaches to derive inviscid multiphase flow…
We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…
In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We…
We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical…
We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a…
The Boussingesq equations was introduced in understanding the coupling nature of the thermodynamics and the fluid dynamics. We show the existence of continuous periodic weak solutions of the Boussinesq equations which satisfies the…
The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides…
In this paper, we investigate the incompressible Navier-Stokes equations coupled with the Vlasov-Fokker-Planck equation, which describes a two-phase mixture of the viscous incompressible fluid with particles or bubbles through a frictional…
This paper concerns the uniqueness of weak solutions to the Cauchy problem to the Ericksen-Leslie system of liquid crystal models in $\mathbb R^2$, with both general Leslie stress tensors and general Oseen-Frank density. It is shown here…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…
We provide some counterexamples concerning the uniqueness and regularity of weak solutions to the initial-boundary value problem for gradient flows of certain strongly polyconvex functionals by showing that such a problem can possess a…
We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we first prove the existence of…
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…
Via convex integration, we construct weak solutions to the non-resistive electron-MHD system which do not conserve energy and magnetic helicity.